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EXAMINATION PAPER: ACADEMIC SESSION 2019/2020
Campus: Medway Faculty Engineering & Science
Level: 5
Exam Session: April/May 2020
MODULE CODE: MECH1081
MODULE TITLE: MECHANICS AND DYNAMICS OF ENGINEERING SYSTEMS
Examination: Type Take Home Exam
SECTION A
Q1.
A high-pressure thick-walled cylindrical vessel, shown in Figure Q1, is carrying pressure of P = 100 MPa. The cylinder has external diameter, D0 = 600 mm and internal diameter, DI = 300 mm. The cylinder is fitted with shut-off valves at the front and back ends of the cylinder.
(a) Determine the maximum shear stress developed in the cylinder. [2 marks]
(b) A routine inspection of the high-pressure cylinders reveals very small crack in the wall of the cylinder at location, Q. To assess the structural integrity of the cylinder, it is necessary to understand the stress state at Q. Therefore, calculate the tangential and radial stresses at Q. Note that point Q is located at a radial distance, r = 250 mm from the centre of the cylinder. [6 marks]
(c) When the shut-off valves are activated, extra axial stresses are experienced at position Q. Determine the magnitude of this extra axial stress, sa . [2 marks] [Total 10 marks]
ANSWER(Purchase full paper to gget all the soluton)
1a)
1b)
1c)
Axial stress =
Q2.
The solid circular steel shaft ABCD shown in Figure Q2 is to be used to transmit power, P from the motor located at D. The solid shaft has an external diameter of 60 mm and at optimal operating condition rotates at a frequency, f = 120 revolutions per minute (rpm). The torque from the motor, TD is used to drive power transmission gears located at positions A, B, and C.
(a) Determine the polar area moment of inertia, J of the solid circular. Take J= pR42 where R = external radius of the solid circular shaft. [2 marks]
(b) If there are no torque losses from the generator to the gear heads at A, B, and C, then determine the unknown torque, TD generated by the electric motor at D. [2 marks]
(c) Calculate the Power, P of the electric motor. Assume Power, P = T w where w =2p f . [3 marks]
(d) Determine the absolute maximum shear stress, tmax in the shaft. Take shear stress, tMAX=TRJ = where T = torque, R = external radius of shaft and J =polar area moment of inertia of shaft. [3 marks] [Total 10 marks]
Q3.
An engine with a mass of 50kg is mounted on a platform which in turn is bolted to the ground. The engine operates at a constant angular velocity of ????????????????????????/???? which gives the platform a steady-state displacement of ????. ????????????. The maximum permissible acceleration for the system must not exceed ???????????? −???? .
Determine:
(a) The transmissibility ratio. [3 marks]
(b) The stiffness of an un-damped isolator which has to be placed between the engine and the platform which will ensure that the acceleration of the system does not exceed ???????????? −???? . [7 marks] [Total 10 marks]
Q4.
Figure Q4 shows a single degree of freedom spring, mass, damper system. The system is such that the ???????????????? mass is attached to a spring with a stiffness of ????????????????????−???? and a damper with a damping coefficient, ???? ????(???????? −1 ) −1 .
If the damped frequency ???????? = ????. ???????? ????????, determine:
(a) The value of the damping coefficient. [5 marks]
(b) The ratio between two successive amplitudes. [5 marks] [Total 10 marks]
Q5.
A wide flange I-section beam, AB of length, L = 2 m is made of steel and designed to support a distributed load, ω0= 5 kN/m. To increase the load-bearing capacity of the beam, it is supported by steel cable, BC as shown in Figure Q5.
(a) By considering the stress element located at position, P, carry out the following evaluations:
(i) Calculate the mean stress, sm of the stress element [2 marks]
(ii) Calculate the radius of the Mohr Circle, R of the stress element [3 marks]
(iii) Calculate the principal shear stresses, s1 and s2 of the stress element. [4 marks]
(iv) Draw a Mohr circle with clearly labelled axes. Indicate on the Mohr circle, the parameters calculated in Q5A(i) to Q5A(iii) above. Finally, mark on the Mohr Circle, the two reference stress states that represent the stress element considered in Figure Q5. [6 marks]
(b) A maintenance engineer, reading off a strain gauge attached at position B of the beam, obtained the x-axis strain, ???????? = ????. ???? × ???????? −???? in the beam. If the steel beam has a rectangular cross-sectional of width, w = 50 mm and height, h = 110 mm, calculate the tension, T in the cable that ensures the structure is in equilibrium. Assume the beam behaves in a linear elastic manner with ???? = ????????. For the steel material, take the Young Modulus, E = 210 GPa. [5 marks] [Total 20 marks]
Q6.
The 6m-long over-hanging beam shown in Figure Q6 represents an arm of a crane-like structure. The structure is pinned at point A but has a roller support at point B. The arm is designed to carry a maximum uniform distributed load, ω = 6kN/m.
(a) Determine the vertical reactions at the supports A and B. [4 marks]
(b) Using the Discontinuity Functions Method, derive the discontinuity function expressions of the beam (assuming origin at point A):
(i) Distributed loading function, ω(x),
(ii) Shear force function, V(x) and
(iii) Bending moment function, M(x). [5 marks]
(c) Draw the shear force diagram of the beam [5 marks]
(d) Draw the bending moment diagram of the beam. [6 marks]
Q7.
Figure Q7 shows a two degree of freedom lumped parameter system where ???????? = ????????????, ???????? = ????????????, ???????? = ????????????????????????−???? ???????????? ???????? = ????????????????????????−???? .
(a) Draw the free body diagrams for each mass and write down the equation of motion for each mass. [6 marks]
(b) For a system where ????(????) = ???? write down the characteristic equation for the system in matrix form and hence determine the two eigenvalues and corresponding eigenvectors. [14 marks]
Q8.
Figure Q8 shows a 4m long simply supported beam. The beam has a constant flexural rigidity of ???????? = ???????????????????????? and carries a uniformly distributed load of ????????????????−???? on its top surface.
(a) Determine the reactions at each of the supports. [2 marks]
(b) Write down the equation for the deflection of the beam [6 marks]
(c) Use Rayleigh’s Method to determine the natural frequency of the system. [12 marks]
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Last updated: Jun 23, 2021 10:57 AM
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